A survey is presented of recent experimental and theoretical researches on the problem of periodic wakes behind a cylinder in a stream. A synopsis is given of the present knowledge on the mechanics of wake formation and of the associated hydrodynamic forces for the full Reynolds number range from the first appearance of a stationary vortex pair behind the cylinder up to transition of the boundary layer on the cylinder. Experimental data are viewed in the light of the theoretical results of Birkhoff, which, it appears, may replace the classical theory based on the first order stability of a potential flow street of vortex filaments. The paper closes with a discussion of the problem of the induced vibration of a spring mounted cylinder in a stream.